https://doi.org/10.1140/epjp/i2011-11076-x
Regular Article
Resonant structure of the early-universe space-time
Institute for Nuclear Research, National Academy of Sciences of Ukraine, 03680, Kiev, Ukraine
* e-mail: maidan@kinr.kiev.ua
Received:
11
April
2011
Revised:
2
June
2011
Accepted:
13
June
2011
Published online:
17
August
2011
A new fully quantum method, describing the propagation of a packet from the internal well outside with its tunneling through a barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method determines amplitudes of the wave function, penetrability T bar and reflection R bar (accuracy of the method is | T bar + R bar -1| < 10−15 , coefficient of penetration (i.e. probability of the packet propagating from the internal well outside), coefficient of oscillations (describing the oscillating behavior of the packet inside the internal well). Using this method, I study the evolution of the universe in the closed Friedmann-Robertson-Walker model with quantization in the presence of positive cosmological constant, radiation and the component of generalized Chaplygin gas. One established for the first time: 1) the oscillating dependence of the penetrability on the localization of the starting point of the packet; 2) the presence of resonant values of the radiation energy E bar , when the coefficient of penetration strongly increases. From the analysis of these results it follows that: 1) an initial condition should be introduced into the non-stationary and stationary quantum models; 2) the start of the expansion of the universe is most probable at some definite values for the scale factor; 3) the radius of the universe has changed non-continuously during its expansion, but it consequently passes through definite discrete values and tends to a continuous range of values at a later time.
© Società Italiana di Fisica and Springer, 2011
